Simplify the following expression: $x = \dfrac{-5p^2 + 45p - 100}{p - 4} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ x =\dfrac{-5(p^2 - 9p + 20)}{p - 4} $ Then we factor the remaining polynomial: $p^2 {-9}p + {20} $ ${-4} {-5} = {-9}$ ${-4} \times {-5} = {20}$ $ (p {-4}) (p {-5}) $ This gives us a factored expression: $\dfrac{-5(p {-4}) (p {-5})}{p - 4}$ We can divide the numerator and denominator by $(p + 4)$ on condition that $p \neq 4$ Therefore $x = -5(p - 5); p \neq 4$